IIT JEE , AIEEE Forum - Mathematics , Algebra - progression---easiest problem

justnitin_1991

A gardner wants to water 50 trees. The first tree is 10 m away from where a well is where he has to fill the water from. There is a gap of 5 m between each tree.
How much distance does he have to cover?
Please anybody explain the solution and remember i don't have the answer with me.
Thank you

Asmita

Here the dis. covered 4 watering the 1st plant & returning back=10m+10m=20m

For the 2nd plant it's 15m+15m=30m

For the 3rd one it's 40m ...........

So total distance=50/2{2*20+49*10}

=13250m

Now we 've 2 subtract the dis. between the 50th plant & the well 2 get the correct ans. which is equal to 10+49*5=255m

So the required ans. is 13250-255=12995m

iitkgp_bipin

Its a simple AP problem.
For the 1st tree distance travelled is (10+10) = 20 m
For 2nd tree = (15+15) = 30 m
For 3rd tree = 40 m ....................and so on

For the 50th tree he only travels from well to tree and not back to well.
Hence for 50th tree distance travelled = 10 + 49*5 = 255 m

Hence distance travelled upto 49th tree = sum of AP
= (49/2)(2*20 + (49-1)*10)
= 12740 m

Hence total distance travelled = 12740 + 255 = 12995 m

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